On subgroups that cover only $\mathfrak F$-central chief factors in finite groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 158-163
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The authors call an element $x$ of a finite group $G$ $Q\mathfrak F$-supercentral if every chief factor $A/B$ of $G$ for which $x\in A\backslash B$ is $\mathfrak F$-central. The connection between $Q\mathfrak F$-supercentral elements of $G$ and its chief factors is investigated. In the case when $\mathfrak F$ is a nonempty saturated formation, the properties of subgroups that cover all $\mathfrak F$-central chief factors of $G$ and isolate all $\mathfrak F$-eccentric chief factors are investigated (the authors call these subgroups $\mathfrak F$-isolators). The connection between $\mathfrak F$-isolators and $\mathfrak F$-normalizers of $G$ is established.
Keywords:
finite group, saturated formation, $Q\mathfrak F$-supercentral element, $\mathfrak F$-normalizer, $\mathfrak F$-isolator.
@article{TIMM_2013_19_3_a15,
author = {S. F. Kamornikov and O. L. Shemetkova},
title = {On subgroups that cover only $\mathfrak F$-central chief factors in finite groups},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {158--163},
publisher = {mathdoc},
volume = {19},
number = {3},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a15/}
}
TY - JOUR AU - S. F. Kamornikov AU - O. L. Shemetkova TI - On subgroups that cover only $\mathfrak F$-central chief factors in finite groups JO - Trudy Instituta matematiki i mehaniki PY - 2013 SP - 158 EP - 163 VL - 19 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a15/ LA - ru ID - TIMM_2013_19_3_a15 ER -
%0 Journal Article %A S. F. Kamornikov %A O. L. Shemetkova %T On subgroups that cover only $\mathfrak F$-central chief factors in finite groups %J Trudy Instituta matematiki i mehaniki %D 2013 %P 158-163 %V 19 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a15/ %G ru %F TIMM_2013_19_3_a15
S. F. Kamornikov; O. L. Shemetkova. On subgroups that cover only $\mathfrak F$-central chief factors in finite groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 158-163. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a15/